We will offer an 8 week REU in geometric analysis/mathematical physics at Brigham Young University (BYU) for 8 students during the summers of 2005, 2006, and 2007. The program will consist of two research groups working with 2 faculty mentors and 1 graduate student assistant. The two research topics will be selected from three areas related to the PI's expertise and experience. These areas are: geometric optimization; minimal surfaces; and mathematical physics. The objectives of this program are: (1) to provide undergraduate students with the opportunity to experience doing mathematical research; (2) to encourage undergraduate students, especially female students and students from institutions with limited research opportunities, to attend graduate school in mathematics; and (3) to prepare participants to be successful in graduate school.